What difference does it make whether Actor and Critic share the same network or not?
One can expect the optimal high-level features required to choose the next action and to evaluate a state to be quite similar. Because of that, it is a reasonable idea to share the same network for both policy and value function – you are essentially parameter sharing the feature-extraction part of your neural network, and fine tuning the different heads of your network on the two different tasks: action choice and value prediction.
Using two vs one networks is mostly a question of sample efficiency: theoretically, in both case your AC algorithm should work. In practice however, it will usually be useful to have parameter sharing as the representations encouraged by one of the tasks might be highly useful for the other and vice-versa, enabling one task to cause the other task to get unstuck from local optima. Another reason why this might work better is simply because you do not have to learn the same (or at least similar) representations from scratch twice – leading to a more sample efficient training.